We investigate the role of a quasiperiodically driven electric field in a disordered fermionic chain. In the clean noninteracting case, we show the emergence of dynamical localization—a phenomenon previously known to exist only for a perfect periodic drive. In contrast, in the presence of disorder, where a high-frequency periodic drive preserves Anderson localization, we show that the quasiperiodic drive destroys it and leads to slow relaxation. Considering the role of interactions, we uncover the phenomenon of quasiperiodic driving-induced logarithmic relaxation, where a suitably tuned drive (corresponding to dynamical localization in the clean, noninteracting limit) slows down the dynamics even when the disorder is small enough for the system to be in the ergodic phase. This is in sharp contrast to the fast relaxation seen in the undriven model, as well as the absence of thermalization (drive-induced many-body localization) exhibited by a high-frequency periodic drive.

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• Anderson localization
• Dynamical localization
• Eigenstate thermalization
• Entanglement entropy
• Localization
• Floquet systems
• Nonequilibrium systems
• Exact diagonalization